1. Field of the Invention
The invention relates to the field of magnetic resonance imaging (MRI) and in particular to optimization of MRI RF sense coil designs for the best signal to noise ratios given a volume of interest and a surface shape on which the coil is to be formed.
2. Description of the Prior Art
Parallel imaging methods have been recently introduced in MRI that allows faster data acquisition using distinct information coming from an array of RF coils. One of these techniques is known as SMASH (Simultaneous Acquisition of Spatial Harmonics). In SMASH a sparsely sampled k-space is collected in the phase encode direction, thus reducing the total image collection time. However, this will cause aliasing in the resulting image. The space between the collected k-space lines are synthesized by forming appropriate linear combinations of the separate information coming from a spatially distributed coil array. This generates gradient induced sinusoidal modulations in the phase encoding direction, thus getting rid of aliasing and obtaining high spatial resolution.
Another popular technique, introduced by Pruessmann et al is known as SENSE (Sensitivity Encoding) imaging. This method also collects a subset of the k-space, but correction is done in image space, instead of synthesizing the k-space lines. Each coil in an array has a different sensitivity to pixels inside the imaging volume. This information is used to decouple separate pixels in overlapping areas inside an aliased image.
Due to non-uniform B1 (RF) field distributions with these coil arrays, the spatial distribution of the signal to noise ratio (SNR) in the images is not uniform. The coil configuration can be optimized to achieve best SNR in the regions of interest. Relative noise images derived from the SENSE theory can be studied to find the optimum coil configuration to minimize noise in the target volume of interest (VOI). These noise images are derived from the coil geometry and reduction factor and they indicate the spatial distribution of relative SNR variations within the imaging volume. The SNR at the pixel location ρ is given by the equationSNRsense,ρ=SNRfull,ρ/(i gρ·√{square root over (R)})  (1)
In equation (1), SNRsense,ρ and SNRfull,ρ represent SNR at pixel location ρ in reduced and full k-space acquisition cases, respectively. Here, gρ is the geometry factor (g-factor) and R is the reduction factor. The geometry factor is determined by the coil configuration and will have a non-uniform distribution inside the imaging volume. Therefore, image noise will also be nonuniformly distributed in the images.
Several groups have attempted to design SENSE optimized coils by taking several coil array configurations and then simulating which topography yielded the smallest g-factor that resulted in the best SNR in a target volume. Weiger et al, and Zwart et al attempted to find optimized SENSE coils by simulating various predefined coil topographies. Similarly, Liffers et al attempted to find optimum phased array coil design for carotid artery imaging by simulating various known coil structures. This approach is restricted by the limited number of coils simulated, and the result will most likely not be the most optimum.
Recently, Dodd et al proposed using simulated annealing to optimize array coil performance. They have designed a four-coil array to demonstrate the method. In this technique, the algorithm starts with a standard rectangular four-coil design and the position of the wires are moved on the surface of the coil former based on a Monte-Carlo type approach. The structure that yields the best SNR is picked as the optimum design. Although this approach may yield a better design compared to other prior approaches, it still has limited scope because the basic design shape still conforms to rectangular geometry and the size of each coil loop is changed to optimize the design.
Coil optimization for particular applications can be achieved by specifying a B1 distribution within a VOI and solving the inverse problem to find the current distribution that will generate the desired field profile. For example, the time-harmonic inverse method was used by Lawrence et al to design an open head and neck RF coil. In this method, the current density on the surface of a selected coil former is defined in terms of a set of basis functions and the magnetic field inside the coil geometry is calculated. Then the inverse problem is solved to obtain a current density distribution that would yield a uniform B1 field inside the coil volume. Later, Xu et al used a similar approach to generate de-emphasized B1 fields inside an unloaded RF coil that would compensate the B1 field nonuniformities caused by the dielectric resonance effects in high magnetic field MRI systems.
In the past, MRI designers have used general-purpose MRI RF coil structures, which were not optimized for accelerated SENSE imaging technique. In sensitivity encoding (SENSE), the effects of inhomogeneous spatial sensitivity of surface coils are utilized for signal localization in addition to common Fourier encoding using magnetic field gradients. Unlike standard Fourier MRI, SENSE images exhibit an inhomogeneous noise distribution, which crucially depends on the geometrical sensitivity relations of the coils used.
In conventional magnetic resonance imaging (MRI), receiver coil arrays are frequently used for the purpose of increasing the signal-to-noise-ratio (SNR). However, parallel signal acquisition with multiple coil elements may be utilized for enhancing imaging speed. Based on knowledge of coil sensitivity, the SENSitivity Encoding technique (SENSE) enables considerable scan time reduction in most currently used MRI techniques. In this method, simultaneously operated coils with inhomogeneous spatial sensitivity are utilized not only for improving base SNR but also for spatial signal encoding complementary to common gradient switching. As a consequence of this additional role of coil sensitivity, SENSE imaging entails specific criteria for the design of coil arrays.
The key goal of MRI coil design is image SNR. In the standard Fourier mode, the use of multiple receiver coils results in enhanced base SNR, varying in the image domain according to the inhomogeneity of net sensitivity. Sensitivity-based reconstruction introduces further spatial variation of SNR. In addition to the common signal intensity variations, local noise enhancement occurs to varying degrees according to the conditioning of the sensitivity based reconstruction steps. Depending strongly on the geometry of the used coil arrangement, this effect has been quantitatively described by the local geometry factor g.
The distribution of g within the desired field-of-view (FOV) directly reflects the specific role of the coil configuration in sensitivity-based reconstruction. Describing the suitability of a coil setup for sensitivity-encoded imaging, it forms the appropriate additional design criterion for SENSE arrays. The geometry factor is a mathematical function of the coil sensitivities and the reduction factor R. However, its structure does not permit straightforward analytical coil optimization, making simulations an indispensable tool in seeking optimized coil arrangements for sensitivity encoding.
Therefore, the signal-to-noise ratio (SNR) was not maximized for SENSitivity Encoding technique (SENSE). Several researchers have tested several basic RF coil designs and among the limited number of units tested, they picked the one with best performance. But none of the designs that were tested had been designed to minimize the geometry factor g of parallel imaging technique to maximize the signal-to-noise ratio. Therefore, this approach does not guarantee the best possible performance among all possible coil designs.
The target field approach was proposed by Turner, “A target field approach to optimal coil design”, J. Phys. D: Appl. Phys., vol. 19, pp. L147-L151, (1986) to design MRI gradient coils. Later, Pissanetzky “Minimum Energy MRI gradient coils of general geometry”, Meas. Sci. Technol., vol. 3, pp. 667-673, (1992) outlined a method that included energy minimization in target field based gradient coil design. In this method, a target magnetic field distribution is specified by the designer and the surface current distribution is calculated to achieve the desired target field. Typically, the surface current distribution on a predefined surface (coil former) is calculated by using a least squares procedure to minimize the difference between the user-defined target field and the field generated by the calculated current distribution.